Rain is falling, vertically with a speed of `1m//s`.Wind starts blowing after sometime with a speed of `1.732 m//s` in east to west direction. In which direction should a boy waiting at a bus stop hold his umbrella?

Explanation

If `R` is the resultant of velocity of rain `(V_(r))` and velocity of wind `(V_(w))` then
`R=sqrt(V_(r)^(2)+V_(w)^(2))=sqrt(1^(2)+(1.732)^(2)ms^(-1))=2ms^(-1)`
The direction `theta` that `R` makes with the vertical is given by `tan theta =V_(w)/V_(v)=sqrt3/1=60^(@)`
Therefore, the boy should hold his umbrealla in the vertical plane at an angle of about `60^(@)` with the vertical towards the east.